458 M. E. Wilde on the Untenableness of 



which values are so exact, that, when set down in the form of 

 a proportion with the square roots found above, the product 

 of the extremes agrees with the product of the means to at 

 least four places of decimals. Thus, for example, for the first 

 and third dark rings, the following proportion ought to hold 

 good, 0-1077 2 : 0*1864 2 = 0*01159 : 0*03474 = 2:6 = 1:3, 

 which it actually does, the product of the extremes agreeing 

 with the product of the means to four places, viz. 0*0347. 



The laws deduced from the undulation theory for the refected 

 light are thus confirmed by experiment^ without its being neces- 

 sary to press the glasses so strongly together as to cause the dark 

 central spot to exhibit itself; and this is the point which it was 

 my object to prove. 



Another consideration which supports the truth of my as- 

 sertion is, that by all analogous phasnomena of colour where, 

 when homogeneous light is used, an alternation of dark and 

 bright is observed, the middle being bright^ the first minimum 

 occurs where the paths traversed by the interfering rays differ 

 by at least an entire undulation. Thus, for example, in the 

 alternation which occurs when light, after having passed 

 through a narrow opening, is received upon an opake screen, 

 the middle, where the difference of path is nothing, is always 

 bright, its intensity being =1. The space however remains 

 also bright when the difference amounts to half an undulation, 

 its intensity at this point being 0*4053, and it is not until the 

 difference amounts to an entire undulation that the first mini- 

 mum occurs*. The resemblance is closer still when the dif- 

 fraction is caused by the rays passing through a small circular 

 opening, in which case the middle is also bright, and the first 

 dark ring occurs where the difference of the paths traversed 

 by the rays is l*220\f. It is, on this account, impossible to 

 determine the difference of path corresponding to the first 

 maximum ring, which appears as a continuation of the bright 

 centre; this difference must be obtained from the expression 

 of intensity (3) ; and for the same reason 1 have been unable 

 to ascertain by measurement the radius of the first bright ring, 

 being obliged also to resort to the expression (3.) to obtain it. 

 Notwithstanding, however, that in all these related phaeno- 

 mena, where the centre is bright, the first minimum does not 

 occur where the difference is half an undulation, still up to 

 the present time it has been assumed, in the case of trans- 

 mitted lights that the centre of Newton's ring-system is bright, 

 and that the first dark ring nevertheless occurs where the 

 depth of the layer of air is one-fourth of an undulation, that 

 is to say, where the difference of paths amounts to half an un- 

 * Poggendorff's Annalen, vol. lxxix. p. 206, f Ibid. p. 224. 



